Sample Problem

36 travelers all want to cross a river, but they only have one boat. If the boat can hold 6 people at a time, how many trips back and forth must they take to carry all 36 travelers across the river?



The first trip will send 6 travelers across the river, but 1 must come back to bring to boat back so each subsequent trip can only send 5 people. After 6 trips, there will be 6´5 = 30 people on the other side of the river. The last 6 people can all go on the same trip, and nobody will need to go back so it will take 7 trips for all the travelers to cross the river.

An important thing to remember while solving these problems is that whenever the boat crosses the river, at least one person must be inside it to row, so if some people cross the river, one must row the boat back for the next trip.